This is an example on how to create a view controller stack in swift.

ViewControllerStack.swift

import UIKit

class ViewControllerStack: UIViewController {
    private var firstContainerTopAnchor: NSLayoutConstraint?
    private var firstController: UIViewController?
    private var controllers: [UIViewController]?
    private var containerView = UIView()
    
    init(controllers: [UIViewController]) {
        self.controllers = controllers
        super.init(nibName: nil, bundle: nil)
    }
    
    required init?(coder _: NSCoder) {
        fatalError("init(coder:) has not been implemented")
    }
    
    override func viewDidLoad() {
        super.viewDidLoad()
        view.backgroundColor = .purple
        containerView.backgroundColor = .gray
        
        containerView.translatesAutoresizingMaskIntoConstraints = false
        view.addSubview(containerView)
        addConstraints(to: containerView, parent: view)

        if let controllers = controllers {
            for controller in controllers {
                addToContainer(viewController: controller, container: containerView)
            }
        }
    }
    
    private func addConstraints(to childView: UIView, parent: UIView) {
        NSLayoutConstraint.activate([
            childView.topAnchor.constraint(equalTo: parent.topAnchor),
            childView.bottomAnchor.constraint(equalTo: parent.bottomAnchor),
            childView.leadingAnchor.constraint(equalTo: parent.leadingAnchor),
            childView.trailingAnchor.constraint(equalTo: parent.trailingAnchor),
        ])
    }
    
    private func sumHeight(_ height: CGFloat) {
        preferredContentSize.height += height
    }
    
    func addToContainer(viewController: UIViewController, container: UIView) {
        addChild(viewController)
        viewController.view.translatesAutoresizingMaskIntoConstraints = false
        container.addSubview(viewController.view)
        
        // Set initial constraints for viewController
        NSLayoutConstraint.activate([
            viewController.view.leadingAnchor.constraint(equalTo: container.leadingAnchor),
            viewController.view.heightAnchor.constraint(equalToConstant: viewController.preferredContentSize.height),
            viewController.view.trailingAnchor.constraint(equalTo: container.trailingAnchor)
        ])
        
        if let firstController = firstController {
            firstContainerTopAnchor?.isActive = false
            firstContainerTopAnchor = nil
            firstController.view.topAnchor.constraint(equalTo: viewController.view.bottomAnchor).isActive = true
        } else {
            viewController.view.bottomAnchor.constraint(equalTo: container.bottomAnchor).isActive = true
        }
        
        firstContainerTopAnchor = viewController.view.topAnchor.constraint(equalTo: container.topAnchor)
        firstContainerTopAnchor?.isActive = true
        
        firstController = viewController
        viewController.didMove(toParent: self)
        sumHeight(viewController.preferredContentSize.height)
    }
}